When a certain type of cell is subjected to radiation, the cell may die, survive as a single cell, or divide into two cells with probabilities 1/2, 1/3, 1/6 respectively.
Two cells are independently subjected to radiation. The random variable X represents the total number of cells in existence after this experiment.
(a) Show that P(X=2) = 5/18
I can do this but I'm not sure of my approach. I drew a tree diagram displaying all possible outcomes and probabilities. Would that be sufficient to answer the question? Are there any other approaches to this type of question?